At an event held at the stadium, 60% of the audience were adults. The female audience was made up of 30% of the adults and 90% of the children. There were 240 more girls than boys.
- How many children went to the stadium in total?
- Some women joined before the event ended, after which 25% of the remaining people at the stadium were women. How many women joined the stadium before it ended?
|
Adults |
Children |
Total |
|
3 u |
2 u |
5 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
0.9 u |
2.1 u |
1.8 u |
0.2 u |
|
Change |
+ ? |
|
+ ? |
After |
|
4.1 u |
|
Comparison in the end |
1 p |
3 p |
4 p |
(a)
60% =
60100 =
35Number of women
= 30% x 3 u
=
30100 x 3 u
= 0.9 u
Number of men
= 3 u - 0.9 u
= 2.1 u
Number of girls
= 90% x 2 u
=
90100 x 2 u
= 1.8 u
Number of boys
= 2 u - 1.8 u
= 0.2 u
Number of more girls than boys
= 1.8 u - 0.2 u
= 1.6 u
1.6 u = 240
1 u = 240 ÷ 1.6 = 150
Number of children
= 2 u
= 2 x 150
= 300
(b)
25% =
25100 =
14The total number of men and children in the end is repeated.
4.1 u = 3 p
Number of men and children
= 2.1 u + 2 u
= 4.1 u
= 4.1 x 150
= 615
3 p = 4.1 u
3 p = 615
1 p = 615 ÷ 3 = 205
Number of women in the end
= 1 p
= 205
Number of women at first
= 0.9 u
= 0.9 x 150
= 135
Number of women who joined before the event ended
= 205 - 135
= 70
Answers: (a) 300; (b) 70